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Estudio Heurístico del Problema Restringido de Tres Cuerpos
Heuristic Study of the Restricted Three Body Problem
Palabras clave:
Enjambre de partículas, integrador, método de Runge Kutta y el problema de tres cuerpos restringido (es)Particle swarm, integrator, Runge Kutta method and the restricted three body problem (en)
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Este artículo presenta una aproximación a uno de los problemas por resolver más importantes que se ha formulado para este siglo. Se consideró el problema de tres cuerpos restringido y se hallaron órbitas periódicas alrededor de los puntos de equilibrio estable entre distintos planetas, donde una nave espacial necesitaría poca energía para moverse. Se implementaron algunas técnicas muy eficientes para la optimización de funciones multivariadas y la integración de ecuaciones diferenciales. Se obtuvieron muy buenos resultados y se muestra que con los métodos usados se reduce el tiempo de computo considerablemente.
This article presents an approach to one of the most important unresolved problems that has been formulated for this century. The restricted three body problem was considered and periodic orbits were found around the points of stable equilibrium between different planets, where a spacecraft would need little energy to move. Some very ecient techniques were implemented for the optimization of multivariate functions and the integration of differential equations. Very good results were obtained and it is shown that the used methods reduce the computing time considerably.
Referencias
A. Albouy and V. Kaloshin, Finiteness of central confgurations of five bodies in the plane., Ann. Math. (2) 176 (2012), no. 1, 535-588 (English).
J. Cerón, J. Amador, and G. Olivar, Dinámica de un sistema lineal en R2 conmutado por histéresis, Ingeniería y Ciencia 13 (2017), 9-28.
B. Conway, Spacecraft trajectory optimization, Cambridge University Press, New York, 2010.
M. Hampton, Finiteness of relative equilibria of the four-body problem, University of Minnesota 5 (2004), 417-435.
M. Hvas, Tuning and simplifying heuristical optimization, University of Southampton, England, 2010.
A. Jorba and M. Zou, A software package for the numerical integration of odes by means of high-order taylor methods, Experiment. Math. 14 (2005), no. 1, 99-117.
A. Jorba and M. Zou, Taylor user's manual, 2008, University of Leeds.
E. P. Konstantinos and M. N. Vrahatis, Particle swarm optimization method for constrained optimization problems, In Proceedings of the Euro-International Symposium on Computational Intelligence 2002, IOS Press, 2002, pp. 214-220.
H. Leeghim, Spacecraft intercept using minimum controlenergy and wait time, Celestial Mechanics and Dynamical Astronomy (2013), 19.
J. Llibre, A note on the dziobek central configurations, Proceedings of the American Mathematical Society 143 (2015), no. 8, 3587-3591.
S. Smale, Mathematical problems for the next century, Mathematical Intelligencer 20 (1998), 7-15.
V. Szebehely and E. Grebenikov, Theory of Orbits-The Restricted Problem of Three Bodies., Soviet Astronomy 13 (1969), 364.
Y. Villanueva, Lagrangian optimization in interplanetary trajectories, Universidad Sergio Arboleda, Colombia, 2013.
